Ec3addformula_Table 5.2 Member subject to bending and compression with test

blueprints/codes/eurocode/en_1993_1_1_2005/chapter_5_structural_analysis/table_5_2_sht1_part_bendcomp.py

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+"""Formula 5.6 from EN 1993-1-1:2005 - Classification of compression parts under bending and compression."""
+
+import numpy as np
+
+from blueprints.codes.eurocode.en_1993_1_1_2005 import EN_1993_1_1_2005
+from blueprints.codes.formula import Formula
+from blueprints.codes.latex_formula import LatexFormula
+from blueprints.type_alias import DIMENSIONLESS, KN, MM, MM2, MPA
+from blueprints.validations import raise_if_less_or_equal_to_zero
+
+
+class Table5Dot2PartSubjecttoBendingandCompression(Formula):
+    """Implements EN 1993-1-1:2005 Table 5.2 (Sheet 1 of 3) for classification of compression parts under bending."""
+
+    label = "5.6"
+    source_document = EN_1993_1_1_2005
+
+    def __init__(self, epsilon: DIMENSIONLESS, c: MM, t_w: MM, n_ed: KN, a: MM2, f_y: MPA) -> None:
+        r"""
+        [$-$] EN 1993-1-1:2005 Table 5.2 (sheet 1 of 3): Maximum widht-to-thickness ratios for compression parts [$-$].
+
+        Parameters
+        ----------
+        epsilon : DIMENSIONLESS
+            [$\epsilon$] Material slenderness factor [$-$].
+        c : MM
+            [$c$] Distance between flange with relation to the Axins of bendingdirection under check [$mm$]
+        t_w : MM
+            [$t_w$] Web thickness [$mm$]. If the web thickness is not constant, t_w should be taken as the minimum thickness.
+        n_ed : kN
+            [$N_{Ed}$] Contains the design axial force [$kN$].
+        A : MM2
+            [$A$] Gross cross-sectional area [$mm^2$].
+        f_y : MPA
+            [$f_y$] Yield strength of the material [$MPa$].
+
+        Returns
+        -------
+        Section Classification
+        """
+        super().__init__()
+        self.epsilon = epsilon
+        self.c = c
+        self.t_w = t_w
+        self.n_ed = n_ed
+        self.a = a
+        self.f_y = f_y
+
+    @staticmethod
+    def _evaluate(epsilon: float, c: MM, t_w: MM, n_ed: KN, a: MM2, f_y: MPA) -> int:
+        """Evaluate section classification based on slenderness ratios."""
+        raise_if_less_or_equal_to_zero(epsilon=epsilon, c=c, t_w=t_w, a=a, f_y=f_y)
+
+        alpha = min(0.5 * (1 + n_ed / (c * t_w * f_y)), 1.0)
+        psi = 2 * n_ed / (a * f_y) - 1
+        c_t_w = c / t_w
+
+        if alpha > 0.5:
+            beta_1w = 396 * epsilon / (13 * alpha - 1)
+            beta_2w = 456 * epsilon / (13 * alpha - 1)
+        else:
+            beta_1w = 36 * epsilon / alpha
+            beta_2w = 41.5 * epsilon / alpha
+
+        beta_3w = 62 * epsilon * (1 - psi) * np.sqrt(abs(psi)) if psi <= -1 else 42 * epsilon / (0.67 + 0.33 * psi)
+
+        if c_t_w <= beta_1w:
+            return 1
+        if c_t_w <= beta_2w:
+            return 2
+        if c_t_w <= beta_3w:
+            return 3
+        return 4  # Slender
+
+    def evaluate(self) -> int:
+        """Compute and return the section classification."""
+        return self._evaluate(self.epsilon, self.c, self.t_w, self.n_ed, self.a, self.f_y)
+
+    def latex(self, n: int = 3) -> LatexFormula:
+        """Return a LatexFormula representation of the section classification."""
+        class_num = self.evaluate()
+        alpha = min(0.5 * (1 + self.n_ed * 1000 / (self.c * self.t_w * self.f_y)), 1.0)
+        psi = 2 * self.n_ed * 1000 / (self.a * self.f_y) - 1
+        c_t_w = self.c / self.t_w
+
+        if alpha > 0.5:
+            beta_1w = 396 * self.epsilon / (13 * alpha - 1)
+            beta_2w = 456 * self.epsilon / (13 * alpha - 1)
+            beta_1_label = r"\alpha > 0.5: \frac{c}{t_w} \leq \frac{396\varepsilon}{13\alpha - 1}"
+            beta_2_label = r"\alpha > 0.5: \frac{c}{t_w} \leq \frac{456\varepsilon}{13\alpha - 1}"
+        else:
+            beta_1w = 36 * self.epsilon / alpha
+            beta_2w = 41.5 * self.epsilon / alpha
+            beta_1_label = r"\alpha \leq 0.5: \frac{c}{t_w} \leq \frac{36\varepsilon}{\alpha}"
+            beta_2_label = r"\alpha \leq 0.5: \frac{c}{t_w} \leq \frac{41.5\varepsilon}{\alpha}"
+
+        beta_3w = 62 * self.epsilon * (1 - psi) * np.sqrt(abs(psi)) if psi <= -1 else 42 * self.epsilon / (0.67 + 0.33 * psi)
+
+        result_label = ["Plastic", "Compact", "Semi-Compact", "Slender"][class_num - 1]
+
+        symbolic_eq = (
+            r"\alpha = \min\left[\frac{1}{2}\left(1 + \frac{N_{Ed}}{d \cdot t_w \cdot f_y}\right),\ 1.0\right] \\"
+            rf"\alpha = {alpha:.{n}f} \\"
+            r"\psi = 2 \cdot \frac{N_{Ed}}{A \cdot f_y} - 1 \\"
+            rf"\psi = {psi:.{n}f} \\"
+            rf"\text{{Class 1: }} {beta_1_label} \\"
+            rf"\text{{Class 2: }} {beta_2_label} \\"
+            rf"\text{{Class 3: }} \frac{{c}}{{t_w}} \leq 62\varepsilon(1 - \psi)\sqrt{{|\psi|}}"
+        )
+
+        numeric_eq = (
+            rf"\beta_{{1w}} = {beta_1w:.{n}f} \\ "
+            rf"\beta_{{2w}} = {beta_2w:.{n}f} \\ "
+            rf"\beta_{{3w}} = {beta_3w:.{n}f} \\ "
+            rf"\frac{{c}}{{t_w}} = {c_t_w:.{n}f} \\ "
+            rf"\text{{Hence, web is Class }} {class_num}: {result_label}"
+        )
+
+        return LatexFormula(
+            return_symbol=r"\text{Web Class}",
+            result=f"Class {class_num}: {result_label}",
+            equation=symbolic_eq,
+            numeric_equation=numeric_eq,
+            comparison_operator_label="\\Rightarrow",
+            unit="-",
+        )

tests/codes/eurocode/en_1993_1_1_2005/chapter_5_structural_analysis/test_table_5_2_sht1_part_bendcomp.py

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+"""Testing Table 5.2 sheet 1 of 3 Part subject to bending and compression of EN 1993-1-1:2005."""
+
+from math import isclose
+
+import pytest
+
+from blueprints.codes.eurocode.en_1993_1_1_2005.chapter_5_structural_analysis.table_5_2_sht1_part_bendcomp import (
+    Table5Dot2PartSubjecttoBendingandCompression,
+)
+
+
+class TestTable5Dot2PartSubjecttoBendingandCompression:
+    """Testing for Table 5.2 sheet 1 of 3 Part subject to bending and compression of EN 1993-1-1:2005."""
+
+    def test_evaluation(self) -> None:
+        """Test evaluation of Table 5.2 sheet 1 of 3 Part subject to bending and compression of EN 1993-1-1:2005."""
+        epsilon = 0.8375
+        c = 799.9
+        t_w = 25.9
+        n_ed = 0.0
+        a = 62200
+        f_y = 335
+
+        # Expected intermediate values
+        expected_alpha = 0.5
+        expected_psi = -1.0
+        expected_beta_1w = 60.3
+        expected_beta_2w = 69.5
+        expected_beta_3w = 103.9
+        expected_c_t_w = 30.9
+
+        form = Table5Dot2PartSubjecttoBendingandCompression(
+            epsilon=epsilon,
+            c=c,
+            t_w=t_w,
+            n_ed=n_ed,
+            a=a,
+            f_y=f_y,
+        )
+
+        result = form.evaluate()
+        assert result == 1, "Expected Class 1 (Plastic) for the given parameters."
+
+        # Manual calculation checks
+        alpha = min(0.5 * (1 + n_ed / (c * t_w * f_y)), 1.0)
+        psi = 2 * n_ed / (a * f_y) - 1
+        c_t_w = c / t_w
+
+        if alpha > 0.5:
+            beta_1w = 396 * epsilon / (13 * alpha - 1)
+            beta_2w = 456 * epsilon / (13 * alpha - 1)
+        else:
+            beta_1w = 36 * epsilon / alpha
+            beta_2w = 41.5 * epsilon / alpha
+
+        beta_3w = 62 * epsilon * (1 - psi) * abs(psi) ** 0.5 if psi <= -1 else 42 * epsilon / (0.67 + 0.33 * psi)
+
+        # Tolerance-based checks
+        assert isclose(alpha, expected_alpha, rel_tol=1e-3)
+        assert isclose(psi, expected_psi, rel_tol=1e-3)
+        assert isclose(beta_1w, expected_beta_1w, rel_tol=1e-2)
+        assert isclose(beta_2w, expected_beta_2w, rel_tol=1e-2)
+        assert isclose(beta_3w, expected_beta_3w, rel_tol=1e-2)
+        assert isclose(c_t_w, expected_c_t_w, rel_tol=1e-2)
+
+    @pytest.mark.parametrize(
+        ("representation", "expected_fragment"),
+        [
+            ("result", "Class 1: Plastic"),
+            ("symbolic_eq", r"\alpha = 0.500"),
+            ("numeric_eq", r"\beta_{1w} = 60.300"),
+        ],
+    )
+    def test_latex(self, representation: str, expected_fragment: str) -> None:
+        """Test LaTeX representation of the section classification."""
+        form = Table5Dot2PartSubjecttoBendingandCompression(
+            epsilon=0.8375,
+            c=799.9,
+            t_w=25.9,
+            n_ed=0.0,
+            a=62200,
+            f_y=335,
+        ).latex()
+
+        # Build actual representation dictionary
+        actual = {
+            "result": form.result,
+            "symbolic_eq": form.equation,
+            "numeric_eq": form.numeric_equation,
+        }
+
+        assert expected_fragment in actual[representation], f"{representation} representation did not contain expected fragment."